"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time, mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, density) and number can be…

After the onset of formal schooling, little is known about the development of children's understanding of the arithmetic concepts of inversion and associativity. On problems of the form a+b-b (e.g., 3+26-26), if children understand the inversion concept (i.e., that addition and subtraction are inverse operations), then no calculations are needed…

Investigates numerical competence in five-month-old infants using a violation-of-expectation paradigm. Supports previous findings that young children possess not only the competence for limited numerical abstraction, but also the ability to carry out addition and subtraction operations. An alternative explanation, that infants' responses are based…

An examination of the status of teaching mathematics to deaf students showed that teachers ignore the hands-on exploration of objects that promotes conceptualization of basic mathematic principles. An arithmetic teaching strategy is proposed which is activity-based and is derived from Piaget's theory of intellectual development in children.…

The monograph presents the findings of a decade long research project on the cognitive learning of children. Several other areas of general significance involved in the work are also treated. These include: (1) the importance of the work to the development of basic learning theory; (2) certain developments in methodology and in a philosophy of…

The experiences of a headmaster of a primary junior school situated in the older part of a large city are described. The point is made that the children in this school, with but little conscious awareness of what was beautiful, had within them an ability to create true beauty within all the media of the arts. This booklet is divided into eight…